Chapter I: Introduction: aspects of "cyberpunkian" quantum field theory
1.5 The theoretical landscape and data science
Figure 1.3: An artist’s creation about the superfluid helium conformal bootstrap project [4] and [5]. The depiction of characters is based entirely on their images in reality. From left to right: Shai Chester, David Meltzer, Junyu Liu, Walter Landry, Alessandro Vichi, David Poland, David Simmons-Duffin, and Ning Su.
Other ingredients include islands (a theoretical physics terminology referring to the isolated region in the theoretical space using the bootstrap method), a spacecraft (referring to the Space Shuttle Columbia experiment), a diagram as stars in the sky (referring to the conformal block expansion, the basics of the bootstrap equation in the conformal field theory). The figure is credited to Jinglin Nicole Gao.
are currently using the most cutting-edge optimization results from the operations research community [39], the current algorithms still have an opportunity for po- tential significant improvement. We also wish to mention that SDP is an extremely useful algorithm that admits a large quantum speedup. Thus, conformal bootstrap might potentially provide clear physical applications for the quantum SDP solver, and will be helpful for benchmarking quantum algorithms and devices [40].
sions or some highly-curved spacetime that humans cannot easily understand. The various counter-intuitive phenomena appearing in the strongly-coupled theory make it more difficult for physicists to control. Some quantum field theories cannot even be precisely defined mathematically. Moreover, quantum field theory can have many parameters and many possible descriptions, which may lead to the same or different predictions. I think, at least for me, many problems cannot be thoroughly studied in my whole life. If I am supposed to give a name for the space of quantum field theories, I will call it thelandscape, a common term used by high energy physicists.
Another difficulty of quantum field theory lies in its experimental difficulty. Probably the best way to verify quantum field theory in the subatomic world is various high- energy physics experiments, especially collider experiments. Experimental results from colliders could verify or expand predictions from some quantum field theories by colliding subatomic particles at some certain energies. This is an extremely complicated process. From the various nuclear resonance states of the low energy collider to the hadron jet on the hadron collider, physics involved in those processes is very difficult to calculate and measure. This often requires a huge amount of engineering and the efforts of countless researchers to achieve.
Perhaps physicists should thank themselves for being in this cyberpunk era. The famous hadron collider, LHC, generates a lot of data every day. A considerable part of the data will be processed by professional data scientists or particle physi- cists. Therefore, big data science is an important means of contemporary particle physics research. For example, machine learning is becoming an important means of processing experimental data of particle physics. In terms of phenomenological theories that are closer to experimental observations, data science has also gradually become an important way to explore the predictions brought by different effective field theories and Wilson parameters, or to simulate experimental data to recon- struct particle resonance states. I here cite two related works on experiment and phenomenology [41, 42]. Interested readers can easily find more works on the Internet.
Here, I prefer to discuss a story that is mainly about formal high energy theory.
Perhaps the most sophisticated networks of quantum field theories are constructed by string theorists. String theory itself could also be understood as a paradigm adapting numerous quantum field theory descriptions. One way to quantify the complexity of string theory is to count its vacua. In some simplest quantum mechanical models, we are familiar with, for instance, hydrogen atoms with Coulomb’s force, the degeneracy
of the vacuum states is usually very few. However, there is potentially a very large amount of vacuum degeneracy in string theory. There are so many choices of microscopic theory, compactification manifold, bundle or brane configuration, flux, etc. Some people believe that the total number of string theory vacua might be finite, and the estimate is usually huge numbers, for instance, 10500(see some early papers, [43–45]).
The gigantic possible choices of string theory vacua seem leading to many different possibilities of physical predictions, for instance, different realizations of effective field theories at low energies, and different possibilities of constants appearing in our universe, for instance, the mass of the electron. The physical interpretation of the string theory landscape and its possible relationship with someillegal theories which could not correspond to any realizations of quantum gravity, are still open problems. People call those the collection of illegal theories theswampland.
The study of string theory landscape and the swampland is a very difficult subject, partially due to the complexity of string theory itself. If we assume that string theory is the Theory of Everything, can it lead to a consistent description of our world and our energy scales, for instance, the standard model? If so, how is it located in the string theory landscape?
Currently, many people are very interested in the so-called swampland program.
This is a research direction that is aiming to possible interpretations of the boundary between the landscape and the swampland (which is called theswampland criterion).
In fact, the space of the swampland is also very large and nontrivial. There are many low energy effective actions that may not be allowed by any formulations of string theories, and it is very important to understand why. Currently, people formulate a large web of conjectures and statements about the landscape and swampland and try to test them by explicit examples, physical or mathematical proofs. (see Figure 1.4).
One of the most important statements among so many swampland conjectures is called theweak gravity conjecture. The statement is that for theories in the landscape allowing gauge symmetry, they have to allow quantum states that are sufficiently charged. Roughly speaking, that is to say, gravity is always weak compared to the electromagnetic force. This could serve as a swampland criterion. In the work [46], with Clifford Cheung and Grant Remmen, we prove this statement for a very generic setup of gravitational theories containing charges. We show that the weak gravity conjecture naturally follows from the saddle point analysis of black hole solutions in the gravitational path integral, which could be partially understood as
Set of consistent low- energy effective Quantum Field Theories String Theory
(Quantum Gravity) Energy scale
Figure 1.4: An illustration of the string theory landscape and the swampland. This is from Figure 1 of [6].
an infrared consistency requirement of the low energy effective description of string theory (The work [46] is presented in Chapter 2 of the thesis).
Despite some partial theoretical success, the landscape is still extremely hard to study. Even if we could formulate conjectures, it is very hard to test them among 10500different vacua. In fact, this huge number is larger than the number of atoms in the whole visible universe. So can we finally study them towards the bottom, and finally find a successful explanation of our universe?
My personal view is that maybe currently some of us could also stick on pure theo- retical research, but eventually, maybe we have to rely on cyberpunkian technologies to find the final answer. The data space is too large, but in an optimistic point of view, I think using data science like technics about machine learning, it is not hopeless to find the answer accurately. Let me give an example of Go. We could roughly count its complexity as the following: notice that the standard Go board has 361 points, so we could have an estimate of possible methods for placing black and white stones as 361! ∼ 10678, which is also a very large number. However, machine learning algorithms could still handle Go right now, and we all remember the famous event in 2016, where the computer program AlphaGo beats the best human player Lee Sedol. Maybe one day, we could use machines to resolve all puzzles in quantum field theory and string theory. One could regard all theoretical efforts we have made now as training data, and currently, we are still mostly trying to produce valuable training data. Eventually, we might need a machine to resolve the puzzle of our universe. I think maybe machines are good at questions of the following type: Can
we predict the probability of obtaining a Standard Model gauge group at low energy inside the string landscape?
In fact, there are already some works about machine learning and string theory. Some of the early comments about string theory landscape and computational complexity are made by Michael Douglas, one of the founders of the concept string theory landscape(see [47–49]). I used to think about a related problem if one could use neural networks to predict random inflationary potentials induced by string landscape in the early universe cosmology when I was an undergrad student in 2014, and write a paper in 2017 [50]. Nowadays, some string theorists and data scientists are now actively initialization collaborations and obtain good results to explore the string theory landscape using cyberpunkian tools (see for instance [51–53]). I feel that it will be great where people might potentially gain great insight inside the landscape from those fancy machines.